Method for making topological insulator structure

ABSTRACT

A method for forming a topological insulator structure is provided. A strontium titanate substrate having a surface (111) is used. The surface (111) of the strontium titanate substrate is cleaned by heat-treating the strontium titanate substrate in the molecular beam epitaxy chamber. The strontium titanate substrate is heated and Bi beam, Sb beam, Cr beam, and Te beam are formed in the molecular beam epitaxy chamber in a controlled ratio achieved by controlling flow rates of the Bi beam, Sb beam, Cr beam, and Te beam. The magnetically doped topological insulator quantum well film is formed on the surface (111) of the strontium titanate substrate. The amount of the hole type charge carriers introduced by the doping with Cr is substantially equal to the amount of the electron type charge carriers introduced by the doping with Bi.

RELATED APPLICATIONS

This application claims all benefits accruing under 35 U.S.C. §119 fromChina Patent Application No. 201210559458.1, filed on Dec. 21, 2012 inthe China Intellectual Property Office, the disclosure of which isincorporated herein by reference. This application is related tocommonly-assigned applications entitled, “METHOD FOR GENERATINGQUANTIZED ANOMALOUS HALL EFFECT,” filed ______ (Atty. Docket No.US50945); “ELECTRICAL DEVICE,” filed ______ (Atty. Docket No. US50947);“TOPOLOGICAL INSULATOR STRUCTURE,” filed ______ (Atty. Docket No.US50946); and “TOPOLOGICAL INSULATOR STRUCTURE,” filed ______ (Atty.Docket No. US50949).

BACKGROUND

1. Technical Field

The present disclosure relates to a method for making topologicalinsulator structure.

2. Discussion of Related Art

If an electric current flows through an electrical conductor in amagnetic field perpendicular to the electric current, a measurablevoltage difference between two sides of the electrical conductor,transverses to the electric current and the magnetic field, will beproduced. The presence of this measurable voltage difference is calledthe Hall effect (HE) discovered by E. H. Hall in 1879. Subsequently, theanomalous Hall effect (AHE) in magnetic materials and the spin Halleffect (SHE) in semiconductors were discovered. Theoretically, HE, AHE,and SHE have corresponding quantized forms. In 1980, K. V. Klitzing etal. achieved quantum Hall effect (QHE) in a semiconductor in a strongmagnetic field at a low temperature (Klitzing K. V. et al., New Methodfor High-Accuracy Determination of the Fine-Structure Constant Based onQuantized Hall Resistance, Phys Rev Lett, 1980, 45:494-497). After that,D. C. Tsui et al. achieved fractional quantum Hall effect (FQHE) duringthe studying of the HE in a stronger magnetic field (Tsui D. C. et al.,Two-Dimensional Magnetotransport in the Extreme Quantum Limit. Phys RevLett, 1982, 48:1559-1562). In 2006, Shoucheng Zhang predicted thatquantum spin Hall effect (QSHE) can be realized in mercurytelluride-cadmium telluride semiconductor quantum wells (Bernevig B. A.et al., Quantum spin Hall effect and topological phase transition inHgTe quantum wells, Science, 2006, 314:1757-1761). This prediction wasconfirmed in 2007 (Konig M. et al. Qauntum spin Hall insulator state inHgTe quantum wells. Science, 2007, 318:766-770). At present, in thevariety of quantized forms of the HE, only the quantum anomalous Halleffect (QAHE) has not been observed in reality. QAHE is the QHE in zeromagnetic field without Landau levels, which can have a Hall resistanceof h/e² (i.e., 25.8 kΩ, i.e., quantum resistance), wherein e is thecharge of an electron and h is Planck's constant. The realizing of theQAHE can get rid of the requirement for the external magnetic field andthe high electron mobility of the sample, and has an applicationpotential in real devices.

Topological insulators (TIs) are a class of new concept quantummaterials. A TI has its bulk band gapped at Fermi level, the same asusual insulators, but hosts gapless, Dirac-type, and spin-split surfacestates at all of its surfaces, which allow the surfaces to beelectrically conductive and are protected by time reversal symmetry(TRS). There are two kinds of TIs, three-dimensional (3D) TIs andtwo-dimensional (2D) TIs. 3D TIs have topologically-protected twodimensional surface states. 2D TIs have topologically-protected onedimensional edge states. The discovery of Bi₂Se₃ group (includingBi₂Se₃, Bi₂Te₃, and Sb₂Te₃) of TIs makes this kind of material receivessubstantial research interest from not only condensed matter physics butalso material science. In 2010, Yu R. et al. predicted that QAHE couldbe achieved in Cr or Fe doped Bi₂Se₃, Bi₂Te₃, and Sb₂Te₃ 3 D TI films(Yu R. et al., Quantized anomalous Hall effect in magnetic topologicalinsulators, Science, 2010, 329:61-64). However, any TI which can observethe QAHE therein has not been achieved. Further, even a ferromagneticmaterial (including magnetic doped TIs) having an anomalous Hallresistance larger than a kiloohm (kΩ) has not been achieved. For a filmhaving a thickness of 5 nanometers and having the anomalous Hallresistance larger than a kiloohm, the corresponding anomalous Hallresistivity should be larger than or equal to 0.5 milliohms·millimeter(mΩ·mm).

What is needed, therefore, is to provide a method for making a TIstructure having a relatively large anomalous Hall resistance.

BRIEF DESCRIPTION OF THE DRAWINGS

Many aspects of the embodiments can be better understood with referencesto the following drawings. The components in the drawings are notnecessarily drawn to scale, the emphasis instead being placed uponclearly illustrating the principles of the embodiments. Moreover, in thedrawings, like reference numerals designate corresponding partsthroughout the several views.

FIG. 1 is a schematic view of a schematic crystal structure of Sb₂Te₃,wherein (a) is a perspective view, (b) is a top view, and (c) is a sideview of 1 QL.

FIG. 2 is a schematic view of an MBE reactor chamber.

FIG. 3 is a scanning tunneling microscope (STM) image of Cr dopedSb₂Te₃.

FIG. 4 is a side view of one embodiment of an electrical device.

FIG. 5 is a top view of one embodiment of the electrical device of FIG.4.

FIG. 6 is a graph showing magnetic field (μ₀H) dependent Hallresistances (R_(yx)) of one embodiment of magnetically doped TI quantumwell film at different back gate voltages (V_(b)), wherein a unit ofR_(yx) is quantum resistance h/e², which is 25.8 kΩ.

FIG. 7 is a graph showing magnetic field (μ₀H) dependent longitudinalresistances (R_(xx)) of the embodiment of FIG. 6 at different back gatevoltages (V_(b)), wherein a unit of R_(xx) is quantum resistance h/e²,which is 25.8 kΩ.

FIG. 8 is a graph showing dependences of R_(yx) and R_(xx) on differentback gate voltages (V_(b)) of the embodiment of FIG. 6, wherein units ofR_(yx) and R_(xx) are both quantum resistance (h/e², i.e., 25.8 kΩ).

FIG. 9 is a graph showing a dependence of arctangent of Hall angle

$\alpha = \frac{R_{yx}}{R_{xx}}$

on different back gate voltages (V_(b)) of the embodiment of FIG. 6.

FIG. 10 is a graph showing magnetic field (μ₀H) dependent Hallresistances (R_(yx)) of another embodiment of magnetically doped TIquantum well film at different back gate voltages (V_(b)), wherein theunit of R_(yx) is kΩ.

FIG. 11 is a graph showing magnetic field dependent longitudinalresistances (R_(xx)) of the embodiment of FIG. 10 at different back gatevoltages (V_(b)), wherein the unit of R_(xx) is kΩ.

FIG. 12 is a graph showing a dependence of Hall angle

$\alpha = \frac{R_{yx}}{R_{xx}}$

on different back gate voltages (V_(b)) of the embodiment of FIG. 10.

FIG. 13 is a graph showing magnetic field (μ₀H) dependent Hallresistances (R_(yx)) of yet another embodiment of magnetically doped TIquantum well film at different back gate voltages (V_(b)), wherein theunit of R_(yx) is quantum resistance (h/e², i.e., 25.8 kΩ).

FIG. 14 is a graph showing magnetic field (μ₀H) dependent longitudinalresistances (R_(xx)) of the embodiment of FIG. 13 at different back gatevoltages (V_(b)), wherein the unit of R_(xx) is quantum resistance(h/e², i.e., 25.8 kΩ).

FIG. 15 is a graph showing a dependence of Hall angle

$\alpha = \frac{R_{yx}}{R_{xx}}$

on different back gate voltages (V_(b)) of the embodiment of FIG. 13.

FIG. 16 is a graph showing magnetic field (μ₀H) dependent Hallresistances (R_(yx)) of a comparative sample (1) at different back gatevoltages (V_(b)), wherein the unit of R_(yx) is Ω.

FIG. 17 is a graph showing a dependence of longitudinal resistance(R_(xx)) on different back gate voltages (V_(b)) of the comparativesample (1) of FIG. 16, wherein the unit of R_(xx) is Ω.

FIG. 18 is a graph showing dependences of R_(yx) and carrier density(n_(2D)) on different back gate voltages (V_(b)) of the comparativesample (1) of FIG. 16, wherein the unit of R_(yx) is Ω.

FIG. 19 is a graph showing magnetic field (μ₀H) dependent Hallresistances (R_(yx)) of a comparative sample (2) at different back gatevoltages (V_(b)), wherein the unit of R_(yx) is Ω.

FIG. 20 is a graph showing magnetic field (μ₀H) dependent Hallresistances (R_(yx)) of a comparative sample (3) at different back gatevoltages (V_(b)), wherein the unit of R_(yx) is Ω.

DETAILED DESCRIPTION

The disclosure is illustrated by way of example and not by way oflimitation in the figures of the accompanying drawings in which likereferences indicate similar elements. It should be noted that referencesto “an” or “one” embodiment in this disclosure are not necessarily tothe same embodiment, and such references mean at least one.

One embodiment of a TI structure is provided. The TI structure includesan insulating substrate and a magnetically doped TI quantum well filmlocated on the insulating substrate. A material of the magneticallydoped TI quantum well film is antimony telluride (Sb₂Te₃) doped bychromium (Cr) and bismuth (Bi) substituting some of the Sb in theSb₂Te₃, which can be represented by a chemical formulaCr_(y)(Bi_(x)Sb_(1-x))_(2-y) Te₃, wherein 0<x<1, 0<y<2. The doping withCr introduces hole type charge carriers and the doping with Biintroduces electron type charge carriers into the magnetically doped TIquantum well film. The values of x and y satisfy that the amount of thehole type charge carriers introduced by the doping with Cr issubstantially equal to the amount of the electron type charge carriersintroduced by the doping with Bi. By satisfying this, the carrierdensity of the magnetically doped TI quantum well film is equal to orsmaller than 1×10¹³ cm⁻² without applying a voltage thereto (i.e., atzero electric field). Thus, the effectiveness of a gate voltage tuningmethod can be guaranteed during realization of the QAHE by themagnetically doped TI quantum well film. The magnetically doped TIquantum well film has 3 QL to 5 QL, and has a thickness in a range from3 QL thickness to 5 QL thickness (about 3 nanometers to about 5nanometers), wherein “QL” means “quintuple layer”. “QL thickness” meansthe thickness of the quintuple layer.

The magnetically doped TI quantum well film is formed by doping theSb₂Te₃ with Cr atoms and Bi atoms to replace some of the Sb atomstherein. Sb₂Te₃ is a layer-type material, belonging to the trigonalcrystal system, and has a space group of D_(3d) ⁵(R 3m). Referring toFIG. 1, on the xy plane, Sb atoms and Te atoms are respectively arrangedin a hexagonal close packing style to form Sb atom layers and Te atomlayers. Sb atom layers and Te atom layers are alternately laminatedalong the direction z perpendicular to the xy plane. Each QL consists offive adjacent atom layers. In Cr_(y)(Bi_(x)Sb_(1-x))_(2-y)Te₃, the fiveadjacent atom layers of one QL are the first Te atom layer (Te1), the Crand Bi doped first Sb atom layer (Sb1), the second Te atom layer (Te2),the Cr and Bi doped second Sb atom layer (Sb1′), and the third Te atomlayer (Te1′). In a single QL, the Sb (or Cr, Bi) atoms and Te atoms arejoined by covalent-ionic bonds. Between adjacent QLs, the Te1 and Te1′are combined by van der Waals force, thus forming cleavage planesbetween adjacent QLs. In Cr_(y)(Bi_(x)Sb_(1-x))_(2-y)Te₃, the values ofx and y satisfy that the amount of the hole type charge carriersintroduced by the doping with Cr is substantially equal to the amount ofthe electron type charge carriers introduced by the doping with Bi. Inone embodiment, 0.05<x<0.3, 0<y<0.3, and 1:2<x:y<2:1 (e.g.,2:3≦x:y≦25:22).

The material of the insulating substrate is not limited, and only needsto be capable of having the magnetically doped TI quantum well filmlocated, grown, and/or formed thereon by a molecular beam epitaxy (MBE)method. In one embodiment, the material of the insulating substrate canhave a dielectric constant greater than 5000 at a temperature equal toor smaller than 10 Kelvin (K), such as strontium titanate (STO). Toachieve a large anomalous Hall resistance, or even achieve the QAHE, achemical potential of the magnetically doped TI quantum well film istuned by applying an external electric field or voltage to themagnetically doped TI quantum well film which is called the gate voltagetuning method. More specifically, the electric field or voltage can beapplied to the magnetically doped TI quantum well film through a topgate and/or a back gate on the TI structure. The chemical potential ofthe magnetically doped TI quantum well film can be tuned by the fieldeffect. To achieve the large anomalous Hall resistance, or even achievethe QAHE, the defects in the magnetically doped TI quantum well filmneed to be as few as possible to decrease the carrier density in themagnetically doped TI quantum well film. However, the top gate is formedby forming a dielectric layer and a metal electrode on a surface of themagnetically doped TI quantum well film, which increases the possibilityof destroying the magnetically doped TI quantum well film or introducingdefects into the magnetically doped TI quantum well film. The insulatingsubstrate, having a relatively large dielectric constant at a relativelylow temperature, can have a relatively large capacitance, though thethickness of the insulating substrate is relatively large. Thus, theinsulating substrate having the relatively large dielectric constant canbe directly used as the dielectric layer at the relatively lowtemperature between the back gate and the magnetically doped TI quantumwell film. The insulating substrate has a first surface and a secondsurface, that is opposite to the first surface. The magnetically dopedTI quantum well film can be formed on the first surface. The back gateis formed by forming a metal electrode on the second surface of theinsulating substrate. The forming of the back gate does not contact tothe magnetically doped TI quantum well film, thus avoids of introducingdefects to the magnetically doped TI quantum well film. When thematerial of the insulating substrate is STO, the magnetically doped TIquantum well film can be grown on a (111) surface, which is used as thefirst surface. The (111) surface is a surface along a (111)crystallographic plane of the STO. The thickness of the STO insulatingsubstrate can be in a range from about 0.1 millimeters to about 1millimeter.

The magnetically doped TI quantum well film can be formed on theinsulating substrate through a molecular beam epitaxy (MBE) method. Oneembodiment of a method for forming the TI structure having the STOsubstrate includes following steps of:

S11, providing the STO substrate having the (111) surface, the STOsubstrate is disposed in a ultra-high vacuum environment in an MEBreactor chamber;

S12, cleaning the surface of the STO substrate by heat-treating the STOsubstrate in the MEB chamber;

S13, heating the STO substrate and forming Bi beam, Sb beam, Cr beam,and Te beam in the MEB chamber in a controlled ratio achieved bycontrolling flow rates of the Bi beam, Sb beam, Cr beam, and Te beam;and

S14, forming the magnetically doped TI quantum well film on the (111)surface of the STO substrate, wherein the controlled ratio of the Bibeam, Sb beam, Cr beam, and Te beam makes that in the magnetically dopedTI quantum well film, the amount of the hole type charge carriersintroduced by the doping with Cr is substantially equal to the amount ofthe electron type charge carriers introduced by the doping with Bi.

In the step S11, the (111) surface of the STO substrate is smooth atatomic level. In one embodiment, the (111) surface of the STO substrateis formed by steps of: cutting the STO substrate along the (111)crystallographic plane; heating the STO substrate in deionized waterbelow 100° C. (e.g., 70° C.); and burning the STO substrate in anenvironment of a combination of O₂ and Ar at a temperature in a rangefrom about 800° C. to about 1200° C. (e.g., 1000° C.). A time period forthe heating in the deionized water can be in a range from about 1 hourto about 2 hours. A time period for the burning in the environment ofthe combination of O₂ and Ar can be in a range from about 2 hours toabout 3 hours.

MEB is a film evaporation-deposition method performed in ultra-highvacuum (in a range from 1.0×10⁻¹¹ mbar to 1.0×10⁻⁹ mbar, e.g., about1.0×10⁻¹⁰ mbar) at a deposition rate in a range from about 0.1 nm/s toabout 1 nm/s to evaporate a source and deposite the film at a low speedwhich allows films to grow epitaxially. The absence of carry gases aswell as the ultra high vacuum environment results in the highestachievable purity of grown films. The MBE reactor chamber can be joinedwith a variable temperature scanning tunneling microscope (VTSTM) andangle resolved photoemission spectroscopy (ARPES) to form a system. Thesystem can have in-situ VTSTM and ARPES tests of the magnetically dopedTI quantum well film.

During the forming of the magnetically doped TI quantum well film andthe VTSTM and ARPES tests of the magnetically doped TI quantum wellfilm, the magnetically doped TI quantum well film is kept in the MBEreactor chamber having a degree of vacuum smaller than 1.0×10⁻¹⁰ mbar (apressure is less than 1.0×10⁻⁸ Pa). In this degree of vacuum, thedensity of the gas molecules at room temperature is about 2.4×10⁶/cm³,and the average distance between the gas molecules is about 0.1millimeters. In this ultra-high vacuum environment, the magneticallydoped TI quantum well film having high purity and few defects can beformed using the MBE method. Meanwhile, in this ultra-high vacuumenvironment, the (111) surface of the magnetically doped TI quantum wellfilm can be kept clean for a long time. In one embodiment, the MBEreactor chamber has a degree of vacuum less than or equal to 5.0×10⁻¹⁰mbar.

In the step S12, the temperature and time of the heat-treating areselected to make the (111) surface of the STO substrate as clean aspossible. In one embodiment, the temperature of the heat-treating isabout 600° C., and the time of the heat-treating is about 1 hour toabout 2 hours. The heat-treating can remove organic substances, gas, andwater adsorbed on the (111) surface of the STO substrate.

In the step S13, the beams of Bi, Sb, Cr, and Te can be generated byheating evaporating sources of Bi, Sb, Cr and Te. FIG. 2 shows that inthe reactor chamber, four independent evaporating sources can bearranged by respectively disposing solid Bi, Sb, Cr, and Te in fourKnudsen cells (K-Cell). One Knudsen cell is composed of a crucible, aheating filament, a water cooling system, an orifice shutter, and athermocouple. A material of the crucible can be pyrolytic boron nitrideor Al₂O₃. The solid Bi, Sb, Cr, and Te are respectively disposed in thecrucibles. All the solid Bi, Sb, Cr, and Te have the purity larger thanor equal to 5N degree (99.999%). The heating filaments (e.g., tantalumfilaments or tungsten filaments) are used to heat the crucibles toevaporate the solid Bi, Sb, Cr, and Te, and the evaporating rate iscontrolled by controlling the heating temperature. The orifice shutteris used to cover the crucible to control the beginning and ending of theevaporation. Thus, the uniformity of the ratio among the Bi, Sb, Cr, andTe in the formed magnetically doped TI quantum well film can becontrolled. The water cooling system is used to decrease the temperaturearound the evaporating source, thus keeps a relatively good vacuum anddecreases the impurity in the MBE reactor chamber. The STO substrate isdisposed in the MEB reactor chamber and spaced from the evaporatingsources. The (111) surface of the STO substrate faces to the evaporatingsources. A heater can be further located on a back side (e.g., near thesecond surface) of the STO substrate opposite to the (111) surface toheat the STO substrate.

The flow rate can be a mass flow rate or a volumetric flow rate, whichis a mass or a volume of a fluid passing through a given surface perunit of time. The flow rates of Bi, Sb, Cr, and Te are represented asV_(Bi), V_(Sb), V_(Cr), and V_(Te) respectively, and satisfyV_(Te)>(V_(Cr)+V_(Bi)+V_(Sb)), to ensure that the magnetically doped TIquantum well film is formed in a Te environment, to decrease the amountof Te vacancies in the magnetically doped TI quantum well film. In oneembodiment, (V_(Cr)+V_(Bi)+V_(Sb)):V_(Te) is in a range from about 1:10to about 1:15. However, the V_(Te) cannot be too large. A relativelylarge V_(Te) tends to induce an aggregation of the Te atoms on the (111)surface of the STO substrate. The V_(Bi), V_(Sb), V_(Cr), and V_(Te) canbe controlled by controlling the temperatures of the four evaporatingsources, and can be measured by a flow meter (e.g., quartz oscillationtype gas flow meter).

In step S14, during the forming of the magnetically doped TI quantumwell film, the STO substrate may need to be heated to a propertemperature (e.g., in a range from about 180° C. to about 250° C.). Thetemperature of the heating of the STO substrate can ensure thedecomposition of Te₂ and/or Te₄ molecule into Te atoms, while ensuringthe formation of a single crystal magnetically doped TI quantum wellfilm. An approximate value of the ratio among the Bi, Sb, Cr, and Te inthe magnetically doped TI quantum well film can be estimated by the flowmeter, and an accurate value can be achieved by chemical elementanalysis of a thick sample (e.g., having a thickness of 100 QL) formedby the same method. In one embodiment, the heating temperature of thesubstrate (T_(sub)) is about 180° C. to about 200° C., the evaporatingtemperature of Te source (T_(Te)) is about 310° C., the evaporatingtemperature of Bi source (T_(Bi)) is about 500° C., the evaporatingtemperature of Sb source (T_(Sb)) is about 360° C., and the evaporatingtemperature of Cr source (T_(Cr)) is about 1020° C. The STO substratecan be heated by tungsten filaments disposed on the back side of the STOsubstrate. In one embodiment, when the magnetically doped TI quantumwell film is a 5 QL film, the first QL of the magnetically doped TIquantum well film is formed at a lower heating temperature of the STOsubstrate (e.g., T_(sub)=180° C.), and the other 4 QL are formed on thefirst QL at a higher heating temperature (e.g., T_(sub)=200° C.). A hightemperature of the STO substrate may cause the surface of the first QLto be uneven. These two temperature periods can ensure that the first QLuniformly and flat on the substrate at a lower temperature, and theother 4 QL can have a high quality at the higher temperature.

After step S14, a step of annealing the magnetically doped TI quantumwell film can be processed to further decrease the defects in themagnetically doped TI quantum well film. The magnetically doped TIquantum well film can be heated at an annealing temperature for anannealing time. In one embodiment, the annealing temperature can be in arange from about 180° C. to about 250° C. (e.g., 200° C.), an annealingtime can be in a range from about 10 minutes to about 1 hour (e.g., 20minutes).

Formation of the TI structure is not limited to the above describedmethod. In another embodiment, the material of the insulating substratecan be Al₂O₃, and the insulating substrate can be a single crystalsapphire substrate. However, because the dielectric constant of sapphireis only about 20 at a low temperature, the sapphire substrate cannot beused as the dielectric layer for the back gate. Thus, the top gatestructure may be used to tune the chemical potential of the magneticallydoped TI quantum well film. More specifically, a solid dielectric layer(e.g., Al₂O₃ film, HfO₂ film, or MgO film) having a small thickness(e.g., 300 nanometers) can be formed on the surface of the magneticallydoped TI quantum well film, and a metal electrode as the top gate canthen be formed on the surface of the dielectric layer.

In another embodiment, to avoid damaging or negatively affecting thestructure of the magnetically doped TI quantum well film, a liquid topgate structure can be used to tune the chemical potential. Morespecifically, a liquid dielectric layer can be formed by dropping a dropof ionic liquid on the surface of the magnetically doped TI quantum wellfilm, and a metal electrode as the top gate can be arranged to be incontact with the liquid dielectric layer but spaced from themagnetically doped TI quantum well film.

As mentioned in the background, Sb₂Te₃ TI film makes it possible torealize the QAHE. Theoretically, Cr can equivalently substitute Sb ofthe Sb₂Te₃ to achieve the Cr doped Sb₂Te₃. The QAHE can be achieved bydoping the Sb₂Te₃ TI film with Cr having an infinite uniformity toachieve the ferromagnetism of the TI film. This ferromagnetism achievedby the doping is different from RKKY type ferromagnetism in traditionaldiluted magnetic semiconductors and does not need charge carriers, thuskeeping the system in the insulating state.

However, the inventors found that in a real system, the carrier densityin the Cr doped Sb₂Te₃ is very large. The carrier density can becalculated by n_(2D)=1/eR_(H), wherein R_(H) is a slope (or gradient) ofa Hall curve (i.e., a curve of magnetic field to Hall resistance). Thetested carrier density of the Sb₂Te₃ quantum well film with Cr doped onSb sites has a carrier density in a scale of 10¹⁴ cm⁻². It is impossibleto tune that large of a carrier density by using either back gatestructure or top gate structure. That large of a carrier density ismainly caused by the defects introduced during the Cr doping of theSb₂Te₃. Numerous factors such as forming conditions and environmentconditions affect the forming of the film. It is extremely difficult todope the Sb₂Te₃ with Cr to the infinite degree of uniformity. During theCr doping, the defects are introduced into the Sb₂Te₃ quantum well film.FIG. 3 shows that an image of Cr doped Sb₂Te₃ at atomic resolutionachieved by VTSTM, the triangle shaped defects are the locations of Crdopants. Theoretically, the substitution of Sb atoms with Cr atoms doesnot introduce extra charge carriers. However, in a real system, thedoping cannot be infinitely uniform. Non-bonded Cr atoms can exist inthe film and introduce extra charge carriers, which is the hole typecharge carriers tested by inventors. The carrier density is too large tobe decreased to a level to realize the QAHE.

In the present disclosure, Sb₂Te₃ is doped by both Cr and Bi to form aquaternary system in the film. The doping of Sb₂Te₃ with Cr and Bi cansimultaneously introduce two adverse types of defects. The defects (holetype) introduced by Cr can be substantially neutralized by the defects(electron type) introduced by another kind of dopant (e.g., Bi), thusdecreasing the carrier density in the material. Thus, the quaternarysystem can have the ferromagnetic property while having a low level ofcarrier density. The amount of Bi doped in the Sb₂Te₃ (i.e., the valueof x in Cr_(y)(Bi_(x)Sb_(1-x))_(2-y)Te₃) depends on the amount ofdefects introduced by Cr. The amount of defects introduced by Cr may beaffected by factors such as forming conditions and environmentalconditions. The amount of defects introduced by Cr can be analyzedpreviously by forming a Cr_(y)Sb_(2-y)Te₃ film under the sameconditions. In one embodiment, 0.05<x<0.3, 0<y<0.2, and 1:2<x:y<2:1(e.g., 2:3≦x:y≦25:22). By adjusting the amount of Bi and Cr (i.e.,adjusting the values of x and y), the amount of the hole type chargecarriers introduced by the doping with Cr is substantially equal to theamount of the electron type charge carriers introduced by the dopingwith Bi, and the carrier density in the magnetically doped TI quantumwell film can be decreased to a level that is capable of being tuned bythe gate tuning method. By using the gate tuning method to tune thequaternary system, the magnetically doped TI quantum well film can havethe carrier density near zero, and have the anomalous Hall resistance(R_(AH)) in a range of 0.3×25.8 kΩ≦R_(AH)≦1×25.81 kΩ (i.e., 7.74kΩ≦R_(AH)≦25.8 kΩ), while the anomalous Hall angle is(α=R_(AH)/R_(xx))≧0.2.

An embodiment of an electrical device based on the TI structure isprovided. The electrical device includes the above described TIstructure. The TI structure includes an insulating substrate including afirst surface and a second surface opposite to the first surface, and amagnetically doped TI quantum well film grown on the first surface ofthe insulating substrate. A material of the magnetically doped TIquantum well film is represented by a chemical formula ofCr_(y)(Bi_(x)Sb_(1-x))_(2-y)Te₃, wherein 0<x<1, 0<y<2. The doping withCr introduces hole type charge carriers and the doping with Biintroduces electron type charge carriers into the magnetically doped TIquantum well film. The values of x and y satisfy that the amount of thehole type charge carriers introduced by the doping with Cr issubstantially equal to the amount of the electron type charge carriersintroduced by the doping with Bi. The magnetically doped TI quantum wellfilm is in a range from 3 QL thickness to 5 QL thickness.

In one embodiment, the electrical device further includes a back gateelectrode and two conducting electrodes (i.e., source electrode anddrain electrode). The back gate electrode is used to tune the chemicalpotential of the magnetically doped TI quantum well film. The twoconducting electrodes are used to conduct an electrical current throughthe magnetically doped TI quantum well film along a first direction.

In one embodiment, the electrical device can further include threeoutput electrodes (e.g., E1, E2 and E3), which are used to test theresistances of the magnetically doped TI quantum well film in the firstdirection (i.e., the longitudinal resistance) and in the seconddirection (i.e., the Hall resistance).

All the above mentioned electrodes can be formed by using an E-beammethod. The material of the electrodes can be selected according tohaving good conductivity (e.g., gold or titanium). In anotherembodiment, the electrodes can be formed by coating an indium paste orsilver paste on the surface of the TI structure.

More specifically, the back gate electrode is located on the secondsurface of the insulating substrate. The two conducting electrodes andthree output electrodes are arranged on the top surface of themagnetically doped TI quantum well film and spaced from each other. Thetwo conducting electrodes and three output electrodes are electricallyconnected to the magnetically doped TI quantum well film. The twoconducting electrodes are arranged at two opposite sides of themagnetically doped TI quantum well film. A line extending from oneconducting electrode to the other conducting electrode is the firstdirection. A line extending from E1 to E2 is the first direction, and aline extending from E2 to E3 is the second direction. The firstdirection is perpendicular to the second direction. The E1, E2 and E3can be arranged at two opposite sides in the second direction of themagnetically doped TI quantum well film. For example, E1 and E2 can bearranged to the same side, and E3 can be arranged on the other side. Thetwo conducting electrodes can be bar shaped with a relatively longlength approximately equal to the length of the magnetically doped TIquantum well film in the second direction. The length direction of theconducting electrodes can be parallel to the second direction. The threeoutput electrodes can be spot electrodes.

Referring to FIG. 4 and FIG. 5, in the figure, x represents the firstdirection and y represents the second direction. In one embodiment ofthe electrical device 10, the magnetically doped TI quantum well film 20formed on the first surface of the insulating substrate 30 has a shapeincluding a rectangular central part 22, two first connecting parts 24extended from the central part 22 to the two conducting electrodes 50,and three second connecting parts 26 extended from the central part 22to the E1, E2, and E3. The three second connecting parts 26 are spacedfrom each other. The length of the central part 22 in the seconddirection is smaller than the length of the conducting electrode 50. Thefirst connecting parts 24 can have a trapezoid shape having two parallelsides parallel to the second direction, the longer one is joined to theconducting electrode 50, the shorter one is joined to the central part22. The three second connecting parts 26 can extend along the seconddirection. In one embodiment, the three second connecting parts 26 canextend from three corners of the rectangle central part 22 to E1, E2,and E3. The back gate electrode 40 is located on the second surface ofthe insulating substrate 30.

The conducting electrode 50 can be located on a top surface of the firstconnecting parts 24 at a side. The pattern of the magnetically doped TIquantum well film 20 having the narrow rectangular central part 22 andthe trapezoid shaped first connecting parts 24 connected to the longconducting electrode 50 can decrease the contacting resistance. Thesecond connecting part 26 can have a strip shape with a narrow width.The output electrode is located on a top surface of the secondconnecting part 26 at one end. The other end of the second connectingpart 26 is joined to the central part 22.

The rectangular central part 22 can have a length of about 100 micronsto about 400 microns (e.g., 200 microns) in the first direction, and alength of about 10 microns to about 40 microns (e.g., 20 microns) in thesecond direction.

The conducting electrode 50 can have a length of about 1 millimeter toabout 4 millimeters (e.g., 2 millimeters) in the second direction, and alength of about 5 millimeters to about 10 millimeters in the firstdirection.

In addition, the electrical device can further include a fourth outputelectrode E4 similar to E1, E2, and E3. E4 is spaced from E1, E2, andE3, and located on a surface of the magnetically doped TI quantum wellfilm 20. A direction from E3 to E4 is the first direction, and adirection from the E1 to E4 is the second direction. Correspondingly,the magnetically doped TI quantum well film 20 can includes four secondconnecting parts 26 respectively extended from the central part 22 toE1, E2, E3, and E4 from the four corners of the central part 22.

The pattern of the magnetically doped TI quantum well film 20 can formedby removing other portion of the magnetically doped TI quantum well film20 by mechanical scraping method, ultraviolet lithography method, orelectron beam lithography method.

An embodiment of a method for generating QAHE includes steps of:

-   -   S21, forming a TI quantum well film in a 3 QL thickness to 5 QL        thickness on the insulating substrate;    -   S22, doping the TI quantum well film with a first chemical        element and a second chemical element during the forming of the        TI quantum well film to form the magnetically doped TI quantum        well film, the doping with the first chemical element and the        second chemical element respectively introducing hole type        charge carriers and electron type charge carriers in the        magnetically doped TI quantum well film, to decrease the carrier        density of the magnetically doped TI quantum well film to be        smaller than or equal to 1×10¹³ cm⁻², one of the first element        and the second element magnetically doping the TI quantum well        film (i.e., one of the first element and the second element is        the magnetically dopant to the topological insulator quantum        well film);    -   S23, applying an electric field to the magnetically doped TI        quantum well film to further decrease the carrier density at        which the QAHE is achieved.

In step S23, when the insulating substrate has a relatively largedielectric constant, the electric field can be applied only by the backgate structure. The electric field can be in a range of ±200V. Step S23can be processed at a low temperature (e.g., smaller than or equal to 10Kelvin (K)). In one embodiment, the step S23 is processed at atemperature smaller than or equal to 1.5 K.

The method for generating QAHE can solve the problem that themagnetically doping of the TI quantum well film (e.g., Cr doping) mayintroduce defects by introducing an adverse type of defects by anotherdopant and applying the electric field, thus effectively decreases thecarrier density to a extremely low level (e.g., below 1×10¹² cm⁻²) torealize QAHE.

Experiments on Some Embodiments

Different embodiments of the electrical devices are formed by usingdifferent magnetically doped TI quantum well films. During an experimentof an electrical device, constant electric current is conducted throughthe magnetically doped TI quantum well film by the two conductingelectrodes at a low temperature. Resistances R_(xx) and R_(yx) indifferent directions of the magnetically doped TI quantum well film aremeasured by using the three output electrodes, wherein R_(xx) is theresistance along the direction of the constant electric current (i.e.,the first direction), and R_(yx) is the resistance along the directionperpendicular to the constant electric current (i.e., the seconddirection). The R_(yx) is the Hall resistance. Top gate structure orback gate structure may be used to tune the chemical potential of themagnetically doped TI quantum well film in the experiment. The top gatevoltage is represented by V_(t), and the back gate voltage isrepresented by V_(b). The magnetic property of the magnetically doped TIquantum well film is studied by a superconducting quantum interferencedevice (SQUID).

In the magnetic materials, R_(yx)=R_(A)M(T,H)+R_(N)H, wherein R_(A) isthe anomalous Hall coefficient, M(T,H) is the magnetization, R_(N) isthe normal Hall coefficient. H is an external magnetic field. The valueof the anomalous Hall resistance is defined as the value of the Hallresistance (R_(yx)) at zero magnetic field. The R_(A)M(T,H) is theanomalous Hall resistance (R_(AH)=R_(A)M(T,H)), which is related to themagnetization (i.e., M(T,H)), and plays the major part of R_(yx) at alow magnetic field. The R_(N)H is the normal Hall resistance, which isthe linear part of R_(yx) at a high magnetic field. R_(N) decides thecarrier density (n_(2D)), and the type of the charge carriers. Thefollowing experiments are processed at near zero magnetic field (i.e.,H=0). Thus, the R_(yx) can be seen as equal to the R_(AH).

Embodiment 1 T=30 mK, 5 QL Sample, Back Gate Structure

The magnetically doped TI quantum well film is 5 QL Cr_(0.15)(Bi_(0.10)Sb_(0.9))_(1.85)Te₃ (i.e., the film has 5 QL), and the substrate 30 isSTO substrate, in the embodiment 1. Different back gate voltages (Vb)are applied to the magnetically doped TI quantum well film, and thecorresponded Hall curves are tested at the temperature of 30 mK.

Referring to FIGS. 6 to 9, H is the magnetization and μ₀ is the vacuumpermeability, in the μ₀H. The unit of μ₀H is Tesla (T). The R_(AH) ofthe sample is changed with V_(b), and the hysteresis phenomena can beseen, which means that the sample has a good ferromagnetic property.When 0V≦V_(b)≦10V, the change of R_(AH) with V_(b) is not very great.When V_(b)=−4.5 V, R_(AH)=25.8 kΩ. The QAHE is realized.

Embodiment 2 T=1.5K, 4 QL Sample, Back Gate Structure

The magnetically doped TI quantum well film is 4 QLCr_(0.22)(Bi_(0.22)Sb_(0.78))_(1.78)Te₃, and the substrate 30 is STOsubstrate, in the embodiment 2.

Different back gate voltages (V_(b)) are applied to the magneticallydoped TI quantum well film, and the corresponded Hall curves are testedat the temperature of 1.5K. Referring to FIG. 10, the hysteresisphenomena can be seen, and the hysteresis loops have a “square” shape,which means that the sample has a great ferromagnetic property. Bychanging V_(b), a relatively large R_(AH) can be achieved. The R_(AH)increases first and then decreases with the increasing of the V_(b).When V_(b)=45 V, R_(AH) reaches the maximum value, which is 10 kΩ. Thisvalue is approximate to 0.4 quantum resistance, the quantum resistanceis 25.8 kΩ. FIG. 11 shows that the R_(xx)−μ₀H curves show a butterflyshaped hysteresis pattern, which also reveals that the sample has agreat ferromagnetic property. In addition, when V_(b)=45V, the anomalousHall angle (α=R_(AH)/R_(xx)) is as high as 0.42, which is twice of thatvalue of the 5 QL sample. FIG. 12 shows that the Hall angle(R_(yx)/R_(xx)) increases first and then decreases with the increasingof the V_(b).

Embodiment 3 T=100 mK, 4 QL Sample, Back Gate Structure

The magnetically doped TI quantum well film is 4 QLCr_(0.22)(Bi_(0.22)Sb_(0.78))_(1.78)Te₃, and the substrate 30 is STOsubstrate, in the embodiment 3.

Different back gate voltages (V_(b)) are applied to the magneticallydoped TI quantum well film, and the corresponded Hall curves are testedat the temperature of 100 mK. FIG. 13 shows that the hysteresisphenomena can be seen, which means that the sample has a goodferromagnetic property. When 0V≦V_(b)≦20V, the change of R_(AH) withV_(b) is not very great. R_(AH) is about 0.6 quantum resistance. WhenV_(b)=10 V, R_(AH) reaches the maximum value, (R_(AH))_(max)=0.59 h·e⁻²,which is about 15.3 kΩ. This value exceeds a half of quantum resistanceand is larger than the greatest known anomalous Hall resistance everachieved in the world at this time. FIG. 14 shows that the change of theR_(xx) with the change of the V_(b) is more obviously than the change ofthe R_(yx) with the change of V_(b) as shown in FIG. 13. Especially,when V_(b)=0V, the anomalous Hall angle (α=R_(AH)/R_(xx))>0.5. FIG. 15shows that the Hall angle (R_(yx)/R_(xx)) increases first and thendecreases with the increasing of the V_(b).

Embodiment 4 T=90 mK, 5 QL Sample, Back Gate Structure, V_(t)=0

The magnetically doped TI quantum well film is 5 QL Cr_(0.15)(Bi_(0.1)Sb_(0.9))_(1.85)Te₃, and the substrate 30 is STO substrate having athickness of 0.25 millimeters, in the embodiment 4. Different back gatevoltages (V_(b)) are applied to the magnetically doped TI quantum wellfilm at the temperature of 90 mK. When V_(b)=30 V, the maximum R_(AH) isabout 24.1 kΩ.

Embodiment 5 T=400 mK, 5 QL Sample, Back Gate Structure, V_(t)=0

The magnetically doped TI quantum well film is 5 QLCr_(0.15)(Bi_(0.1)Sb_(0.9))_(1.85)Te₃, and the substrate 30 is STOsubstrate having a thickness of 0.25 millimeters, in the embodiment 5.Different back gate voltages (V_(b)) are applied to the magneticallydoped TI quantum well film at the temperature of 400 mK. When V_(b)=20V, the maximum R_(AH) is about 23.0 kΩ.

Embodiment 6 T=1.5 K, 5 QL Sample, Back Gate Structure, V_(t)=0

The magnetically doped TI quantum well film is 5 QLCr_(0.15)(Bi_(0.1)Sb_(0.9))_(1.85)Te₃, and the substrate 30 is STOsubstrate having a thickness of 0.25 millimeters, in the embodiment 6.Different back gate voltages (V_(b)) are applied to the magneticallydoped TI quantum well film at the temperature of 1.5 K. When V_(b)=28 V,the maximum R_(AH) is about 19.02 kΩ.

The experiment results of the embodiments 1 to 6 are shown in the Table1.

TABLE 1 Hall V_(b) R_(AH) resistivity, ρ_(yx) R_(xx) No. SampleThickness Temperature (V) (kΩ) (μΩ · m) (kΩ) R_(AH)/R_(xx) 1Cr_(0.15)(Bi_(0.10)Sb_(0.9))_(1.85)Te₃ 5QL  30 mK −4.5 25.8 127.3 3.47.58 2 Cr_(0.22)(Bi_(0.22)Sb_(0.78))_(1.78)Te₃ 4QL 1.5K 45 10 50 23.80.42 3 Cr_(0.22)(Bi_(0.22)Sb_(0.78))_(1.78)Te₃ 4QL 100 mK 10 15.3 76.534 0.45 4 Cr_(0.15)(Bi_(0.1)Sb_(0.9))_(1.85)Te₃ 5QL  90 mK 30 24.1k 1207 3.44 5 Cr_(0.15)(Bi_(0.10)Sb_(0.9))_(1.85)Te₃ 5QL 400 mK 20 23.0 11513 1.7 6 Cr_(0.15)(Bi_(0.10)Sb_(0.9))_(1.85)Te₃ 5QL 1.5K 28 19.02 95.118.88 1.0007

Comparative Examples

(1) Sb_(2-y)Cr_(y)Te₃

By changing the doping amount of Cr, the material of Cr doped Sb₂Te₃ TIquantum well film can be represented as Sb_(2-y)Cr_(y)Te₃. Four samplesof 5 QL Sb_(2-y)Cr_(y)Te₃ TI quantum well films are formed on the (111)surface of the STO substrate, wherein y is 0, 0.05, 0.09, and 0.14respectively. The experiment results reveal that when y=0, Sb_(2-y)Cr_(y)Te₃ is Sb₂Te₃, and 5 QL Sb₂Te₃ has a linear dispersion surfacestate, the Dirac point is located above the Fermi level (E_(F)) and at65 meV. When doping Cr to the Sb₂Te₃, the location of the Dirac pointmoves from +75 meV when y=0.05 to +88 meV when y=0.14. The E_(F) of allthe four samples is not at a magnetically induced gap-opening.

Without Bi doping, the 5 QL Sb_(1.91)Cr_(0.09)Te₃ TI quantum well filmsare tuned by using the back gate structure. FIG. 16 and FIG. 17 showthat R_(xx) always increases with the increasing of V_(b), which is atypical hole type semiconductor behavior. Thus, it can be known that thetuning has no affection to the type of carriers. The carrier type doesnot change during the tuning step. During the tuning step, the mobility(μ) does not change, and bases on the equation R_(xx)⁻¹xx=σ_(xx)=μn_(2D)e, it shows that n_(2D) decreases with the increasingof V_(b) in FIG. 18. FIG. 16 is the Hall curves of the 5 QLSb_(1.91)Cr_(0.09)Te₃ at different V_(b) when T=1.5 K. The voltage rangeof the V_(b) is from about −210 V to about +210 V. The anomalous Hallresistance (R_(AH)) always increases with the increasing of V_(b). WhenV_(b)=−210 V, R_(AH)=24.152, and n_(2D)=3.4×10¹⁴ cm⁻². When V_(b)=+210V,R_(AH)=40.8, and n_(2D)=9.7×10¹³ cm⁻². The relations between R_(AH) andn_(2D) to V_(b) are shown in FIG. 18. It can be seen from the FIG. 18that R_(AH) increases with the decreasing of n_(2D). This phenomenon iscompletely different from the traditional diluted magneticsemiconductors. In the diluted magnetic semiconductor, the larger then_(2D), the larger the R_(AH). However, the R_(AH) is still to low toachieve QAHE.

(2) Bi_(1.78)Cr_(0.22)Se₃

By changing the doping amount of Cr, the material of Cr doped Bi₂Se₃ TIquantum well film can be represented as Bi_(2-y)Cr_(y)Se₃. By selectingy=0.22, the thickness is 10 QL thickness, a sample of 10 QLBi_(1.78)Cr_(0.22)Se₃ TI quantum well film is formed. Referring to FIG.19, when T=1.5K, there is no hysteresis loop observed in the Hall effectexperiment, which indicates that Cr doped Bi₂Se₃ is a paramagneticmaterial. Therefore, the Cr doped Bi₂Se₃ cannot have the QAHE.

(3) Bi_(1.78)Cr_(0.22)Te₃

By changing the doping amount of Cr, the material of Cr doped Bi₂Te₃ TIquantum well film can be represented as Bi_(2-y)Cr_(y)Te₃. By selectingy=0.22, the thickness is 10 QL thickness, a sample of 10 QLBi_(1.78)Cr_(0.22)Te₃ TI quantum well film is formed. FIG. 20 shows thatwhen T=25K, there is hysteresis loops observed in the Hall effectexperiment, which indicates that Cr doped Bi₂Se₃ is a ferromagnetismmaterial.

It is to be understood that the above-described embodiment is intendedto illustrate rather than limit the disclosure. Variations may be madeto the embodiment without departing from the spirit of the disclosure asclaimed. The above-described embodiments are intended to illustrate thescope of the disclosure and not restricted to the scope of thedisclosure.

It is also to be understood that the above description and the claimsdrawn to a method may include some indication in reference to certainsteps. However, the indication used is only to be viewed foridentification purposes and not as a suggestion as to an order for thesteps.

What is claimed is:
 1. A method for forming a topological insulatorstructure comprising following steps of: providing a strontium titanatesubstrate having a surface (111), the strontium titanate substrate isdisposed in a ultra-high vacuum environment in a molecular beam epitaxyreactor chamber; cleaning the surface (111) of the strontium titanatesubstrate by heat-treating the strontium titanate substrate in themolecular beam epitaxy reactor chamber; heating the strontium titanatesubstrate and forming Bi beam, Sb beam, Cr beam, and Te beam in themolecular beam epitaxy chamber in a controlled ratio achieved bycontrolling flow rates of the Bi beam, Sb beam, Cr beam, and Te beam;and forming a magnetically doped topological insulator quantum well filmon the surface (111) of the strontium titanate substrate, in themagnetically doped topological insulator quantum well film, the amountof hole type charge carriers introduced by the doping with Cr issubstantially equal to the amount of electron type charge carriersintroduced by the doping with Bi.
 2. The method of claim 1, wherein amaterial of the magnetically doped topological insulator quantum wellfilm is represented by a chemical formula ofCr_(y)(Bi_(x)Sb_(1-x))_(2-y) Te₃, wherein 0<x<1, 0<y<2, and themagnetically doped topological insulator quantum well film is in a rangefrom 3 QL thickness to 5 QL thickness.
 3. The method of claim 1, wherein0.05<x<0.3, 0<y<0.3, and 1:2<x:y<2:1.
 4. The method of claim 1, whereinthe providing the strontium titanate substrate comprises: cutting thestrontium titanate substrate along the (111) crystallographic plane;heating the strontium titanate substrate in a deionized water; andburning the strontium titanate substrate in an environment comprising O₂and Ar at a temperature in a range from about 800° C. to about 1200° C.5. The method of claim 1, wherein the heat-treating is at about 600° C.for 1 hour to about 2 hours.
 6. The method of claim 1, wherein flowrates of Bi beam, Sb beam, Cr beam, and Te beam are represented asV_(Bi), V_(Sb), V_(Cr), and V_(Te) respectively, and satisfyV_(Te)>(V_(Cr)+V_(Bi)+V_(Sb)).
 7. The method of claim 1, wherein(V_(Cr)+V_(Bi)+V_(Sb)):V_(Te) is in a range from about 1:10 to about1:15.
 8. The method of claim 1, wherein the heating the strontiumtitanate substrate is at a temperature in a range from about 180° C. toabout 250° C.
 9. The method of claim 1, wherein the forming themagnetically doped topological insulator quantum well film comprises:forming a first QL of the magnetically doped topological insulatorquantum well film at a first heating temperature of the strontiumtitanate substrate, and forming other 4 QL on the first QL at a secondheating temperature, wherein the second heating temperature is greaterthan the first heating temperature.
 10. The method of claim 1 furthercomprising an annealing step to the magnetically doped topologicalinsulator quantum well film at an annealing temperature for an annealingtime.
 11. The method of claim 10, wherein the annealing temperature isin a range from about 180° C. to about 250° C.
 12. The method of claim10, wherein the annealing time is in a range from about 10 minutes toabout 1 hour.